Average

Ladakh Prison Department · Mathematics · 56 practice questions with answers and explanations: 18 Easy, 36 Medium, 2 Hard.

Sample questions

Sample Easy question 1

Find the average of 7, 14, 21, 28 and 35.

  1. 21
  2. 18
  3. 19
  4. 20
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Answer: A. Sum = 105, average = 105/5 = 21.

Sample Easy question 2

The average height of 30 boys is 150 cm and of 20 girls is 140 cm. Find the average height of all 50 students.

  1. 146
  2. 145
  3. 147
  4. 144
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Answer: A. Combined average = (30×150 + 20×140)/50 = 7300/50 = 146 cm.

Sample Easy question 3

Find the average of 18, 22, 26, 30 and 34.

  1. 28
  2. 26
  3. 24
  4. 25
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Answer: B. Sum = 130, average = 130/5 = 26.

Sample Medium question 4

The average of x numbers is 15 and the average of y numbers is 28. If the average of all (x + y) numbers is 23, find the ratio x : y.

  1. 8 : 5
  2. 5 : 9
  3. 5 : 8
  4. 3 : 4
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Answer: C. Use the rule of alligation: x : y = (28 − 23) : (23 − 15) = 5 : 8 = 5 : 8.

Sample Medium question 5

The average of x numbers is 30 and the average of y numbers is 45. If the average of all (x + y) numbers is 37, find the ratio x : y.

  1. 1 : 1
  2. 7 : 8
  3. 9 : 7
  4. 8 : 7
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Answer: D. Use the rule of alligation: x : y = (45 − 37) : (37 − 30) = 8 : 7 = 8 : 7.

Sample Medium question 6

The average age of 8 members of a committee is 41 years. When one member aged 18 years is replaced by a new member, the average age rises by 2 years. Find the age of the new member.

  1. 20 years
  2. 34 years
  3. 36 years
  4. 32 years
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Answer: B. Total age increases by 8 × 2 = 16 years, so the new member is 18 + 16 = 34 years old.

Sample Hard question 7

The average of 11 numbers is 50. The average of the first 6 is 49 and of the last 6 is 52. Find the 6th number.

  1. 55
  2. 54
  3. 56
  4. 57
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Answer: C. Sum of all 11 = 550, first 6 sum = 294, last 6 sum = 312. The 6th number is counted in both: 294 + 312 - 550 = 56.

Sample Hard question 8

The average of 12 numbers is 18. If the average of the first 7 is 20 and the average of the last 6 is 15, find the 7th number.

  1. 15
  2. 17
  3. 14
  4. 16
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Answer: B. Total of 12 = 216. First 7 total = 140, last 6 total = 90. 7th number is counted in both groups, so 140 + 90 - 216 = 14 — the 7th number is 14.

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